54
Final review: multiplying and dividing fractions
Textbook, p. 228
GoalReview multiplying and dividing fractions, finding a part of a number and a number from its part.
New words
reciprocal · o‘zaro teskari sonpart of a number · sonning qisminumber from its part · qismiga ko‘ra sonmixed number · aralash son
Explanation
To multiply fractions, multiply numerators and denominators; cancelling first makes the work easier. Division means multiplying by the reciprocal of the divisor: a/b : c/d = a/b · d/c. Mixed numbers are first turned into improper fractions. To find a part of a number, multiply the number by the fraction: 5/8 of 64 is 64 · 5/8 = 40. If the part is known and we need the whole, divide the part by the fraction: if 3/7 of a number is 21, the number is 21 : 3/7 = 49. To avoid mixing the two problems, ask “is the whole or a part being found?”.
Worked examples
1 3/5 · 5/8 = 8/5 · 5/8 = 1. 6 : 3/4 = 6 · 4/3 = 8.
A tank is 3/5 full and holds 45 L. Its capacity is 45 : 3/5 = 45 · 5/3 = 75 L.
Class activity
“Part or whole?”: the teacher reads a problem and the groups sort it as “finding a part: multiply” or “finding the whole: divide”, and then solve it.
Practice
1
Compute 3/4 · 8/9.
2/3
2
Compute 2 1/2 : 5/6.
3
3
A tank holds 45 L when 3/5 full. What is its capacity in litres?
75
4
Why do we multiply by the reciprocal instead of dividing by a fraction?
Multiplying by the reciprocal is equivalent to dividing: dividing by 1/2 is multiplying by 2, since a whole holds two halves.